Physics - Oscillations - Quiz-8

A horizontal platform is executing simple harmonic motion in the vertical direction with frequency f. A block of mass m is placed on the platform. What is the maximum amplitude of the SHM, so that the block is not detached from it?

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$\frac{mg}{2 π^{2} f^{2}}$
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$\frac{mg}{4 π^{2} f^{2}}$
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2. $\frac{g}{2 π^{2} f^{2}}$
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$\frac{g}{4 π^{2} f^{2}}$

A body at the end of a spring executes S.H.M. with a period $T_{1}$ while the corresponding period for another spring is $T_{2}$ . If the period of oscillation with two springs in series is T, then:

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$T = T_{1} + T_{2}$
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$T^{2} = T_{1}^{2} + T_{2}^{2}$
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$\frac{1}{T} = \frac{1}{T_{1}} + \frac{1}{T_{2}}$
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$\frac{1}{T^{2}} = \frac{1}{T_{1}^{2}} + \frac{1}{T_{2}^{2}}$

A body is executing linear S.H.M. At a position x, its potential energy is $E_{1}$ , and at a position y, its potential energy is $E_{2}$ . The potential energy at the position (x + y) is

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$E_{1} + E_{2}$
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$\sqrt{E_{1}^{2} + E_{2}^{2}}$
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$E_{1} + E_{2} + 2 \sqrt{E_{1} E_{2}}$
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$\sqrt{E_{1} E_{2}}$

The equation of a particle executing simple harmonic motion is $y = 0.4 \sin (2 πt + \frac{π}{3})$ (where t is in seconds and y is in meters). The initial phase of the particle is:

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$2 πt + \frac{π}{3}$
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$\frac{π}{3}$
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$\frac{7 π}{3}$
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$\frac{8 π}{3}$

An ideal spring-mass system has a time period of vibration T. If the spring is cut into 4 identical parts and same mass oscillates with one of these parts, then the new time period of vibration will be

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$\frac{T}{2}$
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T
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$\frac{T}{4}$
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2T

The equation of a particle executing simple harmonic motion is $y = 2 \sqrt{2} \sin 314 t .$ Displacement y from the mean position where acceleration becomes zero is: (y is in cm and t is in second)

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2 cm
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0
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$\frac{1}{\sqrt{2}}$ cm
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$2 \sqrt{2}$ cm

The displacement (x) of an S.H.M. varies with time (t) as shown in the figure. The frequency of variation of potential energy is:

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5 Hz
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10 Hz
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40 Hz
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20 Hz

A simple pendulum bob is a hollow sphere full of sand suspended by means of a wire. If all the sand is drained out immediately, then the time period of the pendulum will

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Increase
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Decrease
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Remain the same
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Become erratic

A simple pendulum of length L is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination $θ$ . The time period of the pendulum is

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$T = 2 π \sqrt{\frac{L}{g}}$
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$T = 2 π \sqrt{\frac{L}{g cosθ}}$
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$T = 2 π \sqrt{\frac{L}{g sinθ}}$
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$T = 2 π \sqrt{\frac{L}{g tanθ}}$

A body is placed on a horizontal platform that is undergoing vertical SHM. If the amplitude of oscillation is 40 cm, then the least period of oscillation for which an object placed over the platform is not detached from it is:

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1.256 s
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12.56 s
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0.1256 s
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125.6 s

If a pendulum giving correct time on the ground at a certain place is moved to the top of a tower 320 m high, then the loss in time (in seconds) measured by the pendulum clock in one week is:

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15.12
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7.72
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3.78
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30.24

Instantaneous acceleration (in ${ms}^{- 2}$ ) of a particle executing S.H.M. is given by $a = - \frac{π}{4} \sin (\frac{π}{4} t - \frac{π}{6})$ . The maximum speed of the particle will occur first time at

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1.75 s
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1.4 s
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1.2 s
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0.67 s

A particle moves according to the equation $x = Acos \frac{π}{2} t$ . Distance covered by it in the time interval of t =0 to t =3 s is: (symbols have their usual meanings)

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A
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4A
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3A
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2A

Two simple pendulums of length 1 m and 16 m are in the same phase at the mean position at any instant. If T is the time period of the smaller pendulum, then the minimum time after which they will again be in the same phase will be

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$\frac{3 T}{2}$
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$\frac{3 T}{4}$
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$\frac{2 T}{3}$
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$\frac{4 T}{3}$

A body of mass m hanging with the help of three springs, each of spring constant k as shown. If the mass is slightly displaced and released, then the system will oscillate with the time period

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$2 π \sqrt{\frac{m}{3 k}}$
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$2 π \sqrt{\frac{2 m}{3 k}}$
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$2 π \sqrt{\frac{3 m}{2 k}}$
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$2 π \sqrt{\frac{3 m}{k}}$

The x-t graph of a particle undergoing SHM is shown below. The acceleration of the particle at $t = \frac{4}{3}$ is:

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$\frac{\sqrt{3}}{32} π^{3} cm / s^{2}$
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$- \frac{π^{2}}{32} cm / s^{2}$
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$\frac{π^{2}}{32} cm / s^{2}$
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$- \frac{\sqrt{3}}{32} π^{2} cm / s^{2}$

The position-time (y - t) graph of a particle executing S.H.M. is shown. The time period of the particle is 4 seconds. Equation of particle executing S.H.M. is

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$y = 6 \sin (2 πt + \frac{π}{6})$
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$y = 6 \sin (\frac{π}{2} t + \frac{π}{3})$
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$y = 6 \sin (\frac{π}{2} t + \frac{π}{6})$
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$y = 6 \sin (\frac{π}{2} t - \frac{π}{6})$

A particle starts executing SHM from an extreme position with time period T and amplitude A. The distance travelled by the particle in time $\frac{15 T}{18}$ is:

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3.5 A
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2.5 A
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0.5 A
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1.5

Two tunnels are dug across the earth as shown in the figure. Balls A and B are dropped in the tunnels. If the time period of oscillation of ball A is T, the time period of the oscillation of ball B is :

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T
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$\frac{\sqrt{3}}{2} T$
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$\frac{2}{\sqrt{3}} T$
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$\frac{2}{3} T$

Select the correct statement(s) regarding S.H.M.

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The average speed of particle executing S.H.M. is zero in one complete oscillation.
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The graph between the kinetic and potential energy of a particle executing S.H.M. is a straight line.
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Restoring force acting on the particle is directed towards a fixed point and is directly proportional to the displacement from the mean position of the particle.
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Both (2) & (3)

The graph between the velocity (v) of a particle executing S.H.M. and its displacement (x) is shown in the figure. The time period of oscillation for this SHM will be

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$\sqrt{\frac{α}{β}}$
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$2 π \sqrt{\frac{α}{β}}$
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$2 π (\frac{β}{α})$
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$2 π (\frac{α}{β})$

The displacement of a body performing simple harmonic motion is represented by $x = asin (2 πt + \frac{π}{3})$ . After what approximate time from t = 0, the speed of the particle becomes maximum for the first time?

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0.12 s
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0.24 s
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0.33 s
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0.42 s

A particle is performing S.H.M. with a time period 8 s and starts from the origin. The ratio of distance travelled by a particle in 1st second and 2nd second of its motion is :

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$\sqrt{2}$
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( $\sqrt{2}$ + 1)
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( $\sqrt{2}$ - 1)
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2

Two particles are executing S.H.M. about the same mean position, along the same straight line, with the same amplitude and time period. At any instant, they meet each other at, $- \frac{A}{2}$ while moving in the opposite direction. The phase difference between them is:

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$\frac{2 π}{3}$
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$\frac{π}{3}$
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$\frac{11 π}{6}$
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$\frac{7 π}{6}$

A small block of mass m is kept on a wooden plank which is oscillating in the vertical plane (as shown), with time period T. The amplitude of oscillation at which block leaves contact with the plank is

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$\geq \frac{{gT}^{2}}{4 π}$
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$\leq \frac{{gT}^{2}}{4 π}$
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$\geq \frac{{gT}^{2}}{4 π^{2}}$
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$\leq \frac{{gT}^{2}}{4 π^{2}}$

A particle performing S.H.M. is at rest at points P and Q which are at a distance a and b from point O. It has velocity v when it is halfway between P and Q. The time period of oscillation is:

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$[\frac{b - a}{b \times a}] v$
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$\frac{π (b - a)}{v}$
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$(\frac{b - a}{ba}) v$
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Data is insufficient to answer.

The time period of a simple pendulum in a stationary lift is T. If the lift moves upwards with an acceleration g, then the new time period will be

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Infinite
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$\sqrt{0.6} T$
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$\sqrt{1.67} T$
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0.707T

Acceleration-time (a-t) graph for a particle performing S.H.M. is shown in the figure. Select the incorrect statement.

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Displacement of a particle at A is negative.
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The potential energy of the particle at C is minimum.
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The velocity of the particle at B is positive.
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Speed of particle at D is decreasing.

A particle is executing S.H.M. such that its acceleration 'a' is a function of displacement x as $a = - β (x - 6)$ . The time period of the oscillation is

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$\frac{π}{β}$
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$\frac{π}{2 β}$
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$\frac{2 π}{\sqrt{2} β}$
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$\frac{2 π}{\sqrt{β}}$

A particle of mass 0.5 kg is executing S.H.M. such that its potential energy is 5 J at the mean position. If its total mechanical energy is 9 J and the amplitude of oscillation is 1 cm, then the time period of oscillation of the particle is:

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$\frac{2 π}{100} s$
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$\frac{π}{200} s$
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$\frac{2 π}{25} s$
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$2 π s$

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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